## Learning Math: Patterns, Functions, and Algebra

# Algebraic Thinking

## In this initial session, we will explore algebraic thinking first by developing a definition of what it means to think algebraically, then by using algebraic thinking skills to make sense of different situations.

In This Session

**Part A:** A Framework for Algebraic Thinking

**Part B:** Reasoning About Situations

**Part C:** Qualitative Graphs

**Homework**

In this initial session, we will explore algebraic thinking first by developing a definition of what it means to think algebraically, then by using algebraic thinking skills to make sense of different situations._{1}

### Learning Objectives

In this session, we will introduce you to mathematical thinking tools and algebraic ideas. You will:

- Decide how to describe and represent situations through pictures, charts, graphs, or words
- Interpret and draw conclusions from graphs
- Create graphs to match written descriptions of real-life situations

### Key Terms

**New in This Session:**

algebraic ideas

axes

mathematical thinking tools

representation

### Notes

**Note 1**

The goal of this session is to introduce the notion of algebraic thinking through activities that focus on analytical habits of mind. Because the activities in this session do not require the use of symbolic notation, it may not appear that we are engaged in “formal algebra.”

Nevertheless, we will need to use mathematical thinking tools like problem solving skills, representation skills, and reasoning skills to solve the problems in this session. All of these skills are fundamental to thinking algebraically.

Teachers typically view algebra with a narrow lens, one that focuses on the skills and concepts learned in a traditional Algebra I course. One of the purposes of this session, as well as those that follow, is to broaden our perceptions of what algebra and algebraic thinking are, and to focus on the kind of mathematical thinking and content required to solve problems. The problems in this session were purposely chosen because they are not easily described with symbolic notation. In this way, we can focus on the mathematical thinking tools we are using, as well as representations other than symbolic ones.

Qualitative graphs are also introduced in this session. Working with these graphs will reinforce both the importance of looking globally at situations and the importance of logical and analytical thinking.

**Materials Needed:** Twenty-five counters (chips, tiles, or cubes) per individual working alone or each pair or group when doing the Eric the Sheep activity. (This activity is modeled using the Interactive Activity; individuals or groups may want to use counters in addition to or instead of the activity.)